Hypothesis Tests About a Population Mean, Examples
In the following hypothesis tests, be sure to include all steps.
Example 1:
The U. S. Food and Drug Administration recommends that individuals consume 1000 mg of calcium daily. The International Dairy Foods Association (IDFA) sponsors an advertising campaign aimed at male teenagers to try to increase calcium consumption. After the campaign, the IDFA obtained a random sample of 50 male teenagers and found that the mean amount of calcium consumed was 1081 mg, with a standard deviation of s = 426 mg. Conduct a test to determine whether the campaign was effective. Use the = 0.05 level of significance.
We want to prove that the mean, , calcium consumption for male teenagers after the campaign is greater than the FDA recommendation of 1000 mg per day.
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Example 2:
A student group maintains that the average student must travel for at least 25 minutes in order to reach college each day. The college admissions office obtained a random sample of 31 one-way travel times from students. The sample had a mean of 19.4 min. and a standard deviation of 9.6 min. Does the admissions office have sufficient to reject the students’ claim? Use the level of significance.
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Example 3:
Delco Products, a division of General Motors, produces commutators used in the electrical systems of automobiles. The commutators are designed to be 18.810 mm in overall length. The following random sample of 35 commutator lengths was taken while monitoring the manufacturing process (all data values are in millimeters):
18.80218.81018.78018.75718.82418.82718.825
18.80918.79418.78718.84418.82418.82918.817
18.78518.74718.80218.82518.81018.80218.780 18.830 18.874 18.836 18.758 18.813 18.844 18.861
18.82418.83518.79418.85318.82318.86318.808
Is there sufficient evidence to reject the claim that these parts meet the design requirement “mean length is 18.810 mm?” Use the level of significance.
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Example 4:
Selasphorus platycerus is the scientific name of the broad-tailed hummingbird that is commonly found throughout the western United States. It is known that the mean incubation time for eggs of this bird is approximately 16.5 days (based on information from The Hummingbird Book, by D. Stokes and L. Stokes, Little, Brown and Company). Assume that incubation times are approximately normally distributed. It is suspected that at higher elevations (above 8000 feet), the mean incubation time might be different from 16.5 days. A number of broad-tailed hummingbird nests were located in mountain country above 8000 feet, and incubation times for 18 eggs gave the following information (in days):
1519161618172118171617181916
15212319
Does this information provide sufficient evidence to conclude that the average incubation time for broad-tailed hummingbird eggs at elevations above 8000 feet differs from 16.5 days? Use the α = 0.05 level of significance.
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